Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials

Doha, EHAhmed, HM2020-01-142020-01-142006Cited References in Web of Science Core Collection: 331065-2469https://doi.org/10.1080/10652460500422270https://cutt.ly/YrxTMdUAccession Number: WOS:000238564600003Two formulae expressing explicitly the difference derivatives and the moments of a discrete orthogonal polynomials {P-n(x): Meixner, Kravchuk and Charlier} of any degree and for any order in terms of P-n(x) themselves are proved. Two other formulae for the expansion coefficients of a general-order difference derivatives del(q) f(x), and for the moments x(l)del(q) f(x), of an arbitrary function f (x) of a discrete variable in terms of its original expansion coefficients are also obtained. Application of these formulae for solving ordinary difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica), in order to build and solve recursively for the connection coefficients between two families of Meixner, Kravchuk and Charlier, is described. Three analytical formulae for the connection coefficients between Hahn-Charlier, Hahn-Meixner and Hahn-Kravchuk are also developed.enUniversity for HahnMeixnerKravchuk and Charlier polynomialsexpansion coefficients recurrencerelationslinear difference equationsconnection coefficientsRecurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomialsArticlehttps://doi.org/10.1080/10652460500422270